20120808, 12:23  #1 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2·283 Posts 
Factored vs. Completely factored
In the GIMPS database we can only see if an exponent is "Factored", but it can be difficult to find out wether it has been completely factored or not. On my wishlist is a status called "Completely factored" for those exponents which are proved to be completely factored.
You can find the completely factored Mersenne expos here: http://www.garlic.com/~wedgingt/factoredM.txt So, if I understand it rightly M1061 (now M1277) was previously the smallest expo without know factors, but M929 is yet the smallest exponent which is not completely factored. 
20120808, 13:27  #2 
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 
For some larger exponents, it is possible that the Mersenne numbers have been completely factored, but we will not be able to prove the primality of the cofactor.

20120808, 15:12  #3 
Bemusing Prompter
"Danny"
Dec 2002
California
2×11×107 Posts 
I came up with a similar suggestion two and a half years ago. I agree that there should be some distinction between a fully factored number and one that merely has known factors.
Last fiddled with by ixfd64 on 20120808 at 15:12 
20120808, 15:34  #4  
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2·283 Posts 
Quote:


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